Local existence of strong solutions to micro-macro models for reactive transport in evolving porous media

TL;DR

This paper establishes local-in-time existence of strong solutions for coupled micro-macro models describing reactive transport in evolving porous media, using smooth dependence on geometry and fixed-point methods.

Contribution

It provides the first rigorous local existence results for strongly coupled micro-macro models with evolving geometries in porous media.

Findings

Proved smooth dependence of macroscopic coefficients on micro-scale geometry.

Established local-in-time existence of strong solutions for the coupled system.

Extended results to include bilaterally coupled diffusive transport with level-set geometry.

Abstract

Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenized flow and transport equations are solved on the macroscopic scale, while effective parameters are obtained from auxiliary cell problems on possibly evolving reference geometries (micro-scale). Despite their perspective success in rendering lab/field-scale simulations computationally feasible, analytic results regarding the arising two-scale bilaterally coupled system often restrict to simplified models. In this paper, we first derive smooth-dependence results concerning the partial coupling from the underlying geometry to macroscopic quantities. Therefore, alterations of the representative fluid domain are described by smooth paths of diffeomorphisms. Exploiting the gained regularity of the effective space- and time-dependent macroscopic coefficients, we present local-in-time existence results for strong solutions to the partially coupled micro-macro system using fixed-point arguments. What is more, we extend our results to the bilaterally coupled diffusive transport model including a level-set description of the evolving geometry.